drr {sievetest}

Rosin - Rammler Distribution Functions

Description

Rosin - Rammler model of particle-size distribution and cumulative undersize and oversize distributions used to obtain approximation of of powders or granular materials originated by grinding.

Usage

drr(x, ex, xs)
orr(x, ex, xs)
urr(x, ex, xs)

Arguments

x

particle size, equivalent particle diameter

ex

Rosin - Rammler exponent, measure of the uniformity of grinding

xs

finesse of grinding, that width of mesh associated with a remainder equal to exp(-1) ~ 0.3679

Details

Following functions are used, based on Rosin - Rammler mathematical model of particle-size distribution, for approximation of size distribution.

drr is Rosin - Rammler probability density function
urr is Rosin - Rammler cumulative distribution function (CDF) representing undersize mass fraction
orr is Rosin - Rammler complementary CDF representing oversize mass fraction ie. relative remainder on the sieve with the mesh size x

Rosin - Rammler model (1933) is the Weibull distribution which was proposed by Weibull in 1939, and Weibull distribution functions are part of R.
So the user can use stats::dweibull(x,shape=ex,scale=xs) the same way as drr, and use Weibull distribution functions provided by stats package for deeper analysis.
Similarly, stats::pweibull(x,shape=ex,scale=xs) can be used the same way as urr or
stats::pweibull(x,shape=ex,scale=xs,lower.tail=F) the same way as orr.

Value

Both urr and orr returns value of distribution function.
Function drr returns density.

References

Rinne, H. (2008) The Weibull Distribution: A Handbook, chapter 1.1.2. Taylor & Francis.

See Also

Weibull, plot.std, summary.std

Examples

## The function drr is currently defined as
#  function (x, ex, xs) 
#  {
#      (ex/xs) * (x/xs)^(ex - 1) * exp(-(x/xs)^ex)
#  }

## The function urr is currently defined as
#  function (x, ex, xs) 
#  {
#      1 - exp(-(x/xs)^ex)
#  }

## The function orr is currently defined as
#  function (x, ex, xs) 
#  {
#      exp(-(x/xs)^ex)
#  }


x <- c(1,5,10,50,100)
ex <- 1.386
xs <- 178
stats::dweibull(x,shape=ex,scale=xs)
drr(x,ex,xs)
stats::pweibull(x,shape=ex,scale=xs)
urr(x,ex,xs)
stats::pweibull(x,shape=ex,scale=xs,lower.tail=FALSE)
orr(x,ex,xs)